These are some questions that are considered a little rude in mainstream American culture. In spite of that, you still get people asking questions like these:
How old are you?
How much do you weigh?
Do you have kids?
Why don't you have kids?
Are you married?
Why aren't you married?
How much do you make?
How much rent do you pay?
By the way, if you don't want to answer these questions, you can respond, "I'd rather not say." If that doesn't work, you can say "Mind your own business!"
"How many people are there in your family?" sounds too... er… formal? It's ok, of course. But it does sound a little too much like a question that needs an accurate answer. I think I'd prefer something like, "Do you have any brothers and sisters?" "Come from a big family, do you?" You know, something a bit more casual.
I actually don't like people asking for personal information. Very old-fashioned of me, no doubt. Like Phil says, it's more common to go for the weather, work, and neutral stuff.
I find the question "How many people are in your family?" to be a little confusing because I might not be sure which family you are talking about. Are you asking about the family that I grew up in as a child? Or are you asking about the family that I created as an adult -- do I have a husband and children?
I think a good question for the first type is, "Do you come from a big family?" This gives the other person the freedom to answer in many different ways. They can give a simple yes or no (if it is a topic they don't wish to talk about much), or they can tell you about how many siblings they have, or maybe they'll even want to tell you that they have so many cousins and aunts and uncles that every family reunion is a huge party! Or another question that is fine is: "Do you have many siblings?"
The second type of question is a little more difficult to ask about. Some people are sensitive about being asked if they are married or if they have children. They might feel like other people have expectations that they should have married or had babies by now...and maybe they don't want to, maybe they haven't met the right partner, maybe they are sad because they want to get pregnant or adopt and they have not been fortunate yet, etc.. So I won't usually ask if someone is married or has children immediately after meeting them...and if they do have a spouse or children, they will usually mention these close family members pretty soon in the conversation (mystery solved!).